Riemann Sums and Riemann Sums and Definite IntegralsDefinite IntegralsSection 4.3
xi-1< ci<xiis called a Riemann sum offfor the partition .ci= a + i 1()niiif cx=∆∑∆x∆
Defn. of a Definite IntegralDefn. of a Definite IntegralIf fis defined on the closed interval [a, b] and the limitexists, then fis integrable on [a, b], and the limit is denoted by 01lim()niiif cx∆ →=∆∑01lim()( )bniiiaf cxf x dx∆ →=∆=∑∫
Thm. 4.4 Continuity Implies Thm. 4.4 Continuity Implies IntegrabilityIntegrabilityIf a function fis continuous on the closed interval [a, b], then fis integrable on [a, b].